CN111552003B - Asteroid gravitational field full-autonomous measurement system and method based on ball satellite formation - Google Patents
Asteroid gravitational field full-autonomous measurement system and method based on ball satellite formation Download PDFInfo
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Abstract
The invention discloses a asteroid gravitational field full-autonomous measurement system and method based on a ball satellite formation. The asteroid gravitational field full-autonomous measurement system and the method adopt the formation of the ball satellites to execute the measurement task of the asteroid gravitational field, wherein the main satellite has deep space autonomous navigation and positioning capability, the acquisition of the states such as position, speed and the like can be realized under the condition of not depending on a ground measurement and control network, inter-satellite vector measurement exists between all the auxiliary satellites and the main satellite, and the main satellite can determine the state of the whole formation of the ball satellites according to the running state of the main satellite and the inter-satellite vector measurement result of each auxiliary satellite, so that the formation task which does not depend on the ground measurement and control network can run fully autonomously. In addition, the main satellite and the auxiliary satellites in the ball satellite formation adopt ball satellite configurations, the ball satellite configurations have isotropic characteristics, interference force calculation such as sunlight pressure and the like on the ball satellites is irrelevant to satellite postures, interference force determination accuracy is improved, and accordingly accuracy and resolution of measurement of the asteroid gravitational field are improved.
Description
Technical Field
The invention relates to the technical field of asteroid gravitational field measurement, in particular to a asteroid gravitational field full-autonomous measurement system and method based on ball satellite formation.
Background
The asteroid exploration has important scientific significance and engineering value and is a strategic growth point of future aerospace technology development. The accurate asteroid gravitational field model is the key for the success of the asteroid exploration task and is also the basic physical parameter for the evolution analysis of the asteroid system, the mineral exploration and the exploitation, and the asteroid gravitational field measurement becomes the core technology of the exploration task. Since the 80 s of the last century, the world aerospace major countries successively developed the detection tasks of minor planets, comets and other minor celestial bodies, and so on, for more than ten times. From the aspect of detection form, the asteroid detection task is subjected to the processes of long-distance flying, short-distance flying around, descending landing and sampling return, so that the physical parameters of the asteroid orbit, the material composition, the surface characteristics, the quality, the density and the like are obtained, and the knowledge of human beings on the asteroids is enriched. The asteroid, comet detection tasks that have been and are planned to be carried out are shown in table 1.
TABLE 1 Small celestial body exploration mission that has been implemented and planned to be implemented
From the perspective of the celestial body gravitational field measurement technology, gravitational field measurement modes are track perturbation, star tracking, gravity gradient and the like. Among them, the Asteroid gravitational field measurement developed in the document "J.K. Miller, A.S. Konopliv, P.G. Antrea, et al.determination of Shape, Gravity, and Rotational State of defined 433Eros [ J ] Icarous, 2002,155: 3-17" belongs to the category of orbital perturbation measurement, and an Epson gravitational field model with km of 15 is obtained by inversion according to orbital data of 10 days and 35 heights of the NEAR detector, but the effective order is only 10, and the inversion order of the Epson gravitational field is very low. Because the orbit determination precision of the deep space detector is limited and perturbation influences of interference forces such as sunlight pressure, three-body attraction and the like exist at the same time, the influence of high-order perturbation of the asteroid gravitational field on the detector orbit is submerged in the orbit determination error, the interference force and the like, and thus a high-precision and high-resolution asteroid gravitational field model cannot be obtained through inversion according to the detector perturbation orbit.
In addition, documents "mineral a. carroll, Daniel r. faber. tidal acquisition gradient field from the atomic restriction [ C ].69th International Adaptive Convergence (IAC), Bremen, Germany,1-5October, 2018" propose a method for measuring a minor planet attractive field based on a single accelerometer, which is installed at a position at a certain distance from the satellite centroid, and from which individual components of the gravitational gradient can be deduced, so that the effect of the gravitational gradient at the satellite centroid position is reflected in the accelerometer measurement, and thus used for minor planet attractive field inversion, which is a simplified gravitational gradient measurement mode in practice. Although the gravity gradient measurement mode reduces the requirement on the orbit determination precision of the deep space probe, the accelerometer is eccentrically arranged on the probe, so that the interference force on the mass center of the probe is difficult to obtain, and the measurement precision of the asteroid gravitational field is influenced.
In addition, because the asteroid is far away from the earth, the ground measurement and control and data transmission support capability is poor, and the ground measurement and control has larger time delay, a future asteroid gravitational field measurement system needs to have full autonomous measurement capability to get rid of dependence on a ground measurement and control network, but no research on the aspect exists at present.
Disclosure of Invention
The invention provides a asteroid gravitational field full-autonomous measurement system and method based on ball satellite formation, and aims to solve the technical problems that an existing asteroid gravitational field measurement mode cannot be used for obtaining a high-precision and high-resolution asteroid gravitational field model through inversion and does not have autonomous measurement capability.
According to one aspect of the invention, the full-autonomous measurement system for the asteroid gravitational field based on the formation of the ball satellites comprises a formation of the ball satellites and a ground station, wherein the formation of the ball satellites moves under the action of the asteroid gravitational field, the formation of the ball satellites comprises a main satellite and a plurality of auxiliary satellites, the auxiliary satellites are respectively communicated with the main satellite, the main satellite is communicated with the ground station, and the main satellite is provided with a deep space autonomous navigation positioning system;
each slave satellite is used for measuring an inter-satellite vector between the slave satellite and the master satellite and an inter-satellite distance change rate between the slave satellite and other slave satellites, and transmitting the measurement result to the master satellite;
the main satellite is used for executing formation tasks to operate autonomously based on self autonomous navigation position and speed and inter-satellite vector measurement results of the main satellite and the auxiliary satellites, and transmitting inter-satellite distance change rate measurement results of a plurality of auxiliary satellites to the ground station;
the ground station is used for inverting the asteroid gravitational field according to the received measurement results of the distance change rate between the satellites and establishing an expression of a gravitational field model.
Furthermore, each slave satellite measures through an inter-satellite distance measuring instrument carried by the slave satellite to obtain an observed value of the inter-satellite distance change rate between the slave satellite and other slave satellites, measures through an accelerometer carried by the slave satellite to obtain the self-received interference force or calculates through a high-precision model to obtain the self-received interference force, and then eliminates the influence of the interference force from the observed value of the inter-satellite distance change rate to obtain a true value of the inter-satellite distance change rate under the action of the small planet gravitational field.
Further, the ground station performs orbital integration by selecting a reference asteroid gravitational field model, a satellite perturbation force model and an initial state of a formation satellite, calculates the inter-satellite distance change rate of each satellite and uses the inter-satellite distance change rate as a reference value, and continuously adjusts initial state parameters of the reference asteroid gravitational field model, the satellite perturbation force model and the formation satellite through iteration so that the reference value of the inter-satellite distance change rate continuously approaches a true value, and when the difference between the reference value and the true value of the inter-satellite distance change rate meets a task setting condition, the finally adjusted reference asteroid gravitational field model is the inversion gravitational field model.
Further, the ground station establishes an expression of the asteroid gravitational field model in the following way:
firstly, a coordinate system is established by taking the mass center of the asteroid as an origin, a Brillouin ball which can contain all plastids of the asteroid is established by taking the origin as a sphere center, different gravitational potential expressions and potential coefficients are adopted for regions in the Brillouin ball and regions outside the Brillouin ball, wherein,
the minor planet gravitational potential outside the Brillouin sphere is as follows:
the asteroid gravitational potential in the Brillouin sphere is as follows:
alternatively, the first and second electrodes may be,
the asteroid plastid is divided into a plurality of areas, each area is spherical, then spherical harmonic series expansion is carried out on each area, and then the spherical harmonic series expansion on each area is superposed to obtain a total asteroid gravitational potential function.
Further, the inter-satellite range finder comprises an inter-satellite laser range finder and/or an inter-satellite microwave range finder.
The invention also provides a asteroid gravitational field full-autonomous measurement method based on the formation of the ball satellites, which adopts the asteroid gravitational field full-autonomous measurement system based on the formation of the ball satellites and comprises the following steps:
measuring an inter-satellite vector between each slave satellite and the master satellite and an inter-satellite distance change rate between the slave satellites;
executing formation task autonomous operation based on autonomous navigation position and speed of the main satellite and inter-satellite vector measurement results of the main satellite and the auxiliary satellites;
and inverting the asteroid gravitational field based on the measurement results of the distance change rates among the plurality of satellites, and establishing an expression of a gravitational field model.
Further, the step of measuring the inter-satellite distance change rate between the slave satellites specifically includes the following steps:
measuring an observed value of an inter-satellite distance change rate between the slave satellites by using an inter-satellite distance measuring instrument;
measuring interference force received by the slave star by using an accelerometer or calculating the interference force received by the slave star through a high-precision model;
and eliminating the influence of interference force from the observed value of the change rate of the inter-satellite distance to obtain the true value of the change rate of the inter-satellite distance under the action of the asteroid gravitational field.
Further, the step of inverting the asteroid gravitational field based on the plurality of inter-satellite distance change rate measurement results specifically includes the following steps:
selecting a reference asteroid gravitational field model, a satellite perturbation force model and an initial state of a formation satellite for orbital integration, calculating to obtain the inter-satellite distance change rate of each satellite, and taking the inter-satellite distance change rate as a reference value;
and continuously adjusting the initial state parameters of the reference asteroid gravitational field model, the satellite perturbation force model and the formation satellites in an iterative manner to enable the reference value of the inter-satellite distance change rate to continuously approach the true value, and when the difference between the reference value and the true value of the inter-satellite distance change rate meets the task setting condition, finally adjusting the obtained reference asteroid gravitational field model to be the inversion gravitational field model.
Further, the step of establishing the expression of the gravitational field model specifically includes the following steps:
firstly, a coordinate system is established by taking the mass center of the asteroid as an origin, a Brillouin ball which can contain all plastids of the asteroid is established by taking the origin as a sphere center, different gravitational potential expressions and potential coefficients are adopted for regions in the Brillouin ball and regions outside the Brillouin ball, wherein,
the minor planet gravitational potential outside the Brillouin sphere is as follows:
the asteroid gravitational potential in the Brillouin sphere is as follows:
further, the step of establishing the expression of the gravitational field model specifically includes the following steps:
the asteroid plastid is divided into a plurality of areas, each area is spherical, then spherical harmonic series expansion is carried out on each area, and then the spherical harmonic series expansion on each area is superposed to obtain a total asteroid gravitational potential function.
The invention has the following effects:
the asteroid gravitational field full-autonomous measurement system based on the ball satellite formation adopts the ball satellite formation to execute the asteroid gravitational field measurement task, wherein the main satellite has deep space autonomous navigation and positioning capability, the acquisition of the states such as position, speed and the like can be realized under the condition of not depending on a ground measurement and control network, inter-satellite vector measurement exists between all the auxiliary satellites and the main satellite, and the main satellite can determine the state of the whole ball satellite formation according to the self running state and the inter-satellite vector measurement result of each auxiliary satellite, so that the formation task full-autonomous running independent of the ground measurement and control network is realized. In addition, the main satellite and the auxiliary satellites in the ball satellite formation adopt ball satellite configurations, the ball satellite configurations have isotropic characteristics, interference force calculation such as sunlight pressure and the like on the ball satellites is irrelevant to satellite postures, interference force determination accuracy is improved, and accordingly accuracy and resolution of measurement of the asteroid gravitational field are improved.
In addition, the asteroid gravitational field full-autonomous measurement method based on the formation of the spherical satellites has the advantages.
In addition to the objects, features and advantages described above, other objects, features and advantages of the present invention are also provided. The invention is explained in further detail below with reference to the drawing.
Drawings
The accompanying drawings, which are incorporated in and constitute a part of this application, illustrate embodiments of the invention and, together with the description, serve to explain the invention and not to limit the invention. In the drawings:
fig. 1 is a schematic diagram of a asteroid gravitational field fully autonomous measurement system based on formation of spherical satellites according to a preferred embodiment of the invention.
FIG. 2 is a schematic diagram of the iterative adjustment of a ground station during inversion of a gravitational field in accordance with a preferred embodiment of the present invention.
Fig. 3 is a schematic diagram of a method for modeling the asteroid gravitational field partitioned spherical harmonic series expansion adopted by the ground station according to the preferred embodiment of the invention, wherein a single brillouin sphere is used for containing all the plastids of the asteroid.
Fig. 4 is a schematic diagram of a plurality of regions respectively containing asteroid plastids by using a plurality of brillouin spheres in the asteroid gravitational field partitioning spherical harmonic series expansion modeling method adopted by the ground station in the preferred embodiment of the invention.
Fig. 5 is a schematic flow chart of a method for fully autonomously measuring a asteroid gravitational field based on formation of spherical satellites according to another embodiment of the invention.
Fig. 6 is a sub-flowchart of step S1 in fig. 5.
Fig. 7 is a sub-flowchart of step S3 in fig. 5.
Detailed Description
The embodiments of the invention will be described in detail below with reference to the accompanying drawings, but the invention can be embodied in many different forms, which are defined and covered by the following description.
As shown in fig. 1, the preferred embodiment of the present invention provides an asteroid gravitational field fully autonomous measurement system based on a formation of ball satellites, which includes a formation of ball satellites moving under the action of a asteroid gravitational field and a ground station disposed on the earth. The formation of the ball satellite comprises a main satellite and a plurality of auxiliary satellites, wherein the main satellite and the auxiliary satellites both adopt ball satellite configurations, the ball satellite configurations have isotropic characteristics, interference force calculation such as sunlight pressure and the like on the ball satellites is irrelevant to satellite postures, and the interference force determination precision is improved, so that the precision and the resolution of the measurement of the asteroid gravitational field are improved. The plurality of slave satellites are respectively communicated with the master satellite, the master satellite is communicated with the ground station, and the master satellite is loaded with a deep space autonomous navigation positioning system, such as an astronomical navigation system, an inertial navigation system, an image navigation system or other navigation system loads such as a combined navigation system thereof, so that the master satellite has full autonomous navigation positioning capability. In addition, the main satellite is also loaded with data transmission loads to realize the communication between the main satellite and the ground station. The slave satellite is provided with an accelerometer for measuring interference force received by the slave satellite, and is also provided with an inter-satellite distance meter and a data transmission load, wherein the data transmission load is used for realizing data communication between the slave satellite and the master satellite, the inter-satellite distance meter is used for measuring the inter-satellite distance change rate between the slave satellite and is used as core data for gravitational field inversion, and simultaneously, the inter-satellite vector between the slave satellite and the master satellite can be measured and is used as support data for the all-autonomous running of the formation of the spherical satellite. It will be appreciated that the master and slave stars are externally covered with solar panels to provide energy support for the operation of each satellite. Each slave satellite transmits an inter-satellite vector measurement result between the slave satellite and the master satellite and an inter-satellite distance change rate measurement result between the slave satellite and other slave satellites to the master satellite, and the master satellite can obtain the position and the speed of the whole formation of the spherical satellites based on the self-independent navigation position and speed and the inter-satellite vector measurement results of the master satellite and the slave satellites, so that the formation of the spherical satellites can obtain state information such as the position and the speed of each satellite without the support of a ground measurement and control network, and the full-independent operation of a formation task is realized. And the main satellite also transmits the received inter-satellite distance change rate measurement results of the plurality of slave satellites back to the ground station, because the data processing process of inversion of the asteroid gravitational field has huge calculation amount, the requirements of huge data processing amount and calculation amount can be met only by performing inversion at the ground station, and the ground station inverts the asteroid gravitational field according to the received inter-satellite distance change rate measurement results of the plurality of slave satellites and establishes an expression of a gravitational field model. In addition, fig. 1 illustrates an example in which 1 master star and 3 slave stars form a global satellite formation, and the number of the slave stars is not particularly limited.
It can be understood that, in the asteroid gravitational field fully autonomous measurement system based on the formation of the spherical satellites according to the preferred embodiment, the formation of the spherical satellites is adopted to execute the measurement task of the asteroid gravitational field, wherein the master satellite has deep space autonomous navigation and positioning capability, the acquisition of the states such as position, speed and the like can be realized under the condition of not depending on a ground measurement and control network, inter-satellite vector measurement exists between all slave satellites and the master satellite, and the master satellite can determine the state of the whole formation of the spherical satellites according to the running state of the master satellite and the inter-satellite vector measurement results of the master satellite and the slave satellites, so that the formation task fully autonomous running independent of the ground measurement and control network is realized. In addition, the main satellite and the auxiliary satellites in the ball satellite formation adopt ball satellite configurations, the ball satellite configurations have isotropic characteristics, interference force calculation such as sunlight pressure and the like on the ball satellites is irrelevant to satellite postures, interference force determination accuracy is improved, and accordingly accuracy and resolution of measurement of the asteroid gravitational field are improved.
It will be appreciated that the inter-satellite rangefinder comprises an inter-satellite laser rangefinder and/or an inter-satellite microwave rangefinder. And each slave satellite measures through an inter-satellite distance meter carried by the slave satellite to obtain an observed value of the inter-satellite distance change rate between the slave satellite and other slave satellites, measures through an accelerometer carried by the slave satellite to obtain the self-received interference force or calculates through a high-precision model to obtain the self-received interference force, wherein the high-precision model can adopt a sunlight pressure model, a three-body gravitation model and the like, and then eliminates the influence of the interference force from the observed value of the inter-satellite distance change rate, so that the true value of the inter-satellite distance change rate under the action of the pure asteroid gravitational field is obtained and serves as core data of a subsequent inversion asteroid gravitational field. Because the satellite adopts a spherical satellite configuration, the calculation of interference forces such as sunlight pressure and the like received by the spherical satellite is irrelevant to the satellite attitude, so that the interference forces received by the satellite can be accurately obtained through the accelerometer or the high-precision model, accurate data support is provided for the subsequent inversion gravitational field, and the measurement precision and resolution of the asteroid gravitational field are improved.
It can be understood that, after the ground station receives the inter-satellite distance change rate measurement results of a plurality of slave satellites transmitted by the master satellite, the ground station performs orbital integration by selecting an initial state of a reference asteroid gravitational field model, a satellite perturbation force model and a formation satellite, calculates to obtain the inter-satellite distance change rate of each slave satellite and uses the inter-satellite distance change rate as a reference value, and then iteratively and continuously adjusts initial state parameters of the reference asteroid gravitational field model, the satellite perturbation force model and the formation satellite, so that the reference value of the inter-satellite distance change rate is continuously close to a true value, and when the difference between the reference value and the true value of the inter-satellite distance change rate meets a task setting condition, the finally adjusted reference asteroid gravitational field model is an inversion gravitational field model. It can be understood that the task setting condition may be set according to actual needs, for example, a difference between a reference value of the inter-satellite distance change rate obtained by calculation and a real value obtained by measurement is required to be smaller than a certain threshold.
Specifically, assuming that there is an inter-satellite range between any two spherical satellites i and j in the formation, the observation equation for inverting the asteroid gravitational field based on the rate of change of the inter-satellite range can be expressed as:
wherein the content of the first and second substances,
wherein the residual error
Obtained by subtracting the reference value and the true value of the rate of change of the inter-satellite distance, the subscripts i and j indicate that the variable is related to the satellites i and j, and Delta X0,i、ΔX0,jThe initial state correction amounts (including position correction amount, velocity correction amount, and the like) of the satellites i and j are provided, and Δ P is the correction amount of the median coefficient in the asteroid gravitational field model. r isi、
Are respectively the position, velocity vector, r, of the satellite ij、
Respectively, the position and velocity vectors of the satellite j, ρ ═ ri-rjI is the distance between the satellites i, j, YX,i(t) is a matrix of partial derivatives of the satellite i position vector with respect to its initial position, initial velocity,
is a partial derivative matrix of the satellite i velocity vector to its initial position and initial velocity, YP,i(t) is a matrix of partial derivatives of the satellite i position vector against the kinetic parameter vector,
is a partial derivative matrix of a velocity vector of the satellite i to a kinetic parameter vector, and the partial derivative matrix and the kinetic parameter vector jointly form a state transition matrix phi of the satellite ii(t) and a parameter sensitivity matrix Si(t) of (d). Similarly, for satellite j, YX,j(t)、
YP,j(t)、
Form the state transition matrix Φ for satellite jj(t) and a parameter sensitivity matrix Sj(t), specifically as follows:
by solving the matrix Ψi(t)、Ψj(t) obtaining YX,i(t)、
YP,i(t)、
And YX,j(t)、
YP,j(t)、
And the matrix Ψi(t)、Ψj(t) satisfies the following differential equation:
initial conditions are Ψi(t0)＝(I6×606×k)、Ψj(t0)＝(I6×6 06×k). Wherein 0 is a zero matrix, I is an identity matrix,
acceleration of motion, t, of satellites i, j, respectively0The method is characterized in that the method is an initial moment of formation motion of the spherical satellites, P is a column vector formed by bit coefficients in a asteroid gravitational field model, and the number of the bit coefficients is k.
Aiming at the true values of all the inter-satellite distance change rates in the formation of the ball satellites, establishing an observation equation as shown in the formula (1), combining the observation equations to obtain a measurement observation equation set of the asteroid gravitational field of the formation of the ball satellites, and solving the equation set to obtain a asteroid gravitational field model. Specifically, as shown in FIG. 2, the residuals
The difference is obtained by the reference value and the true value of the change rate of the distance between the satellites, and the coefficient of the equation set [ (D)1)ij (D2)ij (D3)ij]Then solving the real observation value based on the formulas (2) to (10), and solving the equation set to obtain the initial state correction quantity delta X of the satellites i and j0,i、ΔX0,jAnd correcting quantity delta P of the median coefficient in the asteroid gravitational field model. Then adding the correction quantities to the initial state vector of the formation satellite and the reference asteroid gravitational field model respectively to obtain a new initial state of the formation satellite and the reference asteroid gravitational field model, repeating the above process for continuous iteration,and calculating the difference between the reference value and the true value of the inter-satellite distance change rate to meet the task setting condition until the bit coefficient precision of the obtained asteroid gravitational field model meets the requirement.
Unlike celestial bodies with regular shapes, such as the earth and the moon, the shape and mass distribution of the asteroid can be irregular, so that the distribution of the gravitational field of the asteroid is irregular. The asteroid gravitational potential function based on the conventional spherical harmonic series expansion expression is as follows:
wherein (r, theta and lambda) are spherical coordinates of the mass point on the asteroid in the body coordinate system, r is the distance from the mass point to the origin of the coordinate system, theta is the included angle between the vector of the origin pointing to the mass point and the positive direction of the z axis, and lambda is the included angle between the projection vector of the origin pointing to the mass point in the xy plane and the positive direction of the x axis. G is a universal gravitation constant, M is the asteroid mass, a is the radius of the Brillouin sphere,
is the coefficient of the gravitational potential of the minor planet,
is a fully normalized associative legendre polynomial. Although the spherical harmonic series expansion method has the advantages of analytic expression, high calculation speed and convenience in theoretical analysis, a large number of regions are located in the Brillouin sphere region near the asteroid, and the spherical harmonic series in the regions are likely to be divergent, so that the application of the spherical harmonic series expansion method is limited. In order to solve the problem, the invention provides a method for modeling an asteroid irregular gravitational field based on partition spherical harmonic series expansion, which specifically comprises two methods. In the first method, considering that the asteroid gravitational potential function is a harmonic function, and the fundamental form of the harmonic function is different in the spherical region and outside the spherical region, the space outside the asteroid is divided into two regions, i.e. the Brillouin spherical region and the spherical region, and the spherical harmonic series expansion in the two regions takes different expressionsEquation and bit coefficient. Specifically, in the asteroid gravitational field inversion process, the ground station adopts a asteroid gravitational field partitioning spherical harmonic series expansion modeling method for establishing an analytical expression of the asteroid gravitational field model.
As shown in fig. 3, a coordinate system is first established with the centroid of the asteroid as the origin, a minimum sphere, i.e., brillouin sphere, which can contain all the masses of the asteroid is established with the origin as the sphere center, different expressions and bit coefficients are adopted for the regions inside and outside the brillouin sphere, wherein,
the minor planet gravitational potential outside the Brillouin sphere is as follows:
the asteroid gravitational potential in the Brillouin sphere is as follows:
wherein, K1、K2As a coefficient, on the brillouin sphere, there is Vout(r,θ,λ)＝Vin(r, theta, lambda) and the phenomenon of spherical harmonic series divergence can be avoided by developing the representation method according to the asteroid gravitational field partition spherical harmonic series.
In the second method, as shown in fig. 4, the asteroid plastid is divided into several regions, each region is approximately spherical, preferably spherical, then the spherical harmonic series expansion is performed for each region, and then the spherical harmonic series expansions in the respective regions are superimposed to obtain the total asteroid gravitational potential function. Therefore, the part of the external region of the asteroid, which falls in the Brillouin spherical region, can be greatly reduced, and the gravitational potential in the region near the asteroid is ensured to be converged when being subjected to spherical harmonic series expansion.
The two methods can obtain the asteroid gravitational field spherical harmonic series expansion method, and the obtained asteroid gravitational field subarea spherical harmonic series expansion method is convergent in the external area of the asteroid.
In addition, it can be understood that, as shown in fig. 5, another embodiment of the present invention further provides a asteroid gravitational field fully autonomous measurement method based on a ball satellite formation, preferably using the asteroid gravitational field fully autonomous measurement system based on a ball satellite formation as described above, where the asteroid gravitational field fully autonomous measurement method based on a ball satellite formation includes the following steps:
step S1: measuring an inter-satellite vector between each slave satellite and the master satellite and an inter-satellite distance change rate between the slave satellites;
step S2: executing formation task autonomous operation based on autonomous navigation position and speed of the main satellite and inter-satellite vector measurement results of the main satellite and the auxiliary satellites;
step S3: and inverting the asteroid gravitational field based on the measurement results of the distance change rates among the plurality of satellites, and establishing an expression of a gravitational field model.
The inter-satellite vector between the slave satellite and the master satellite and the inter-satellite distance change rate between the slave satellite and other slave satellites are measured by the inter-satellite distance measuring instrument carried by each slave satellite, and the measurement result is uniformly transmitted to the master satellite by each slave satellite. The main satellite can obtain the position and the speed of the whole formation of the ball satellite based on the self autonomous navigation position and speed and the inter-satellite vector measurement result of the main satellite and the auxiliary satellite, so that the formation of the ball satellite can obtain the state information such as the position and the speed of each satellite without the support of a ground measurement and control network, and the full autonomous operation of a formation task is realized. And the main satellite also transmits the received inter-satellite distance change rate measurement results of the plurality of slave satellites back to the ground station, because the data processing process of inversion of the asteroid gravitational field has huge calculation amount, the requirements of huge data processing amount and calculation amount can be met only by performing inversion at the ground station, and the ground station inverts the asteroid gravitational field according to the received inter-satellite distance change rate measurement results of the plurality of slave satellites and establishes an expression of a gravitational field model.
It can be understood that, in the asteroid gravitational field fully-autonomous measurement method based on the formation of the spherical satellites according to the embodiment, the formation of the spherical satellites is adopted to execute the measurement task of the asteroid gravitational field, wherein the master satellite has deep space autonomous navigation and positioning capability, the acquisition of the states such as position, speed and the like can be realized under the condition of not depending on a ground measurement and control network, inter-satellite vector measurement exists between all the slave satellites and the master satellite, and the master satellite can determine the state of the whole formation of the spherical satellites according to the running state of the master satellite and the inter-satellite vector measurement results of the master satellite and the slave satellites, so that the formation task fully-autonomous running independent of the ground measurement and control network is realized. In addition, the main satellite and the auxiliary satellites in the ball satellite formation adopt ball satellite configurations, the ball satellite configurations have isotropic characteristics, interference force calculation such as sunlight pressure and the like on the ball satellites is irrelevant to satellite postures, interference force determination accuracy is improved, and accordingly accuracy and resolution of measurement of the asteroid gravitational field are improved.
It can be understood that, as shown in fig. 6, the step of measuring the inter-satellite distance change rate between the slave satellites in the step S1 specifically includes the following steps:
step S11: measuring an observed value of an inter-satellite distance change rate between the slave satellites by using an inter-satellite distance measuring instrument;
step S12: measuring interference force received by the slave star by using an accelerometer or calculating the interference force received by the slave star through a high-precision model;
step S13: and eliminating the influence of interference force from the observed value of the change rate of the inter-satellite distance to obtain the true value of the change rate of the inter-satellite distance under the action of the asteroid gravitational field.
It can be understood that, as shown in fig. 7, the step of inverting the asteroid gravitational field based on the several inter-satellite distance change rate measurements in step S3 specifically includes the following steps:
step S31: selecting a reference asteroid gravitational field model, a satellite perturbation force model and an initial state of a formation satellite for orbital integration, calculating to obtain the inter-satellite distance change rate of each satellite, and taking the inter-satellite distance change rate as a reference value;
step S32: and continuously adjusting the initial state parameters of the reference asteroid gravitational field model, the satellite perturbation force model and the formation satellites in an iterative manner to enable the reference value of the inter-satellite distance change rate to continuously approach the true value, and when the difference between the reference value and the true value of the inter-satellite distance change rate meets the task setting condition, finally adjusting the obtained reference asteroid gravitational field model to be the inversion gravitational field model. The specific iterative adjustment process has been described in detail in the above preferred embodiment, and therefore, is not described herein again.
It can be understood that the step of establishing the expression of the gravitational field model in step S3 specifically includes the following steps:
firstly, a coordinate system is established by taking the mass center of the asteroid as an origin, a Brillouin ball which can contain all plastids of the asteroid is established by taking the origin as a sphere center, different gravitational potential expressions and potential coefficients are adopted for regions in the Brillouin ball and regions outside the Brillouin ball, wherein,
the minor planet gravitational potential outside the Brillouin sphere is as follows:
the asteroid gravitational potential in the Brillouin sphere is as follows:
it is to be understood that in another embodiment of the present invention, the step of establishing the expression of the gravitational field model includes the following:
the asteroid plastid is divided into a plurality of areas, each area is spherical, then spherical harmonic series expansion is carried out on each area, and then the spherical harmonic series expansion on each area is superposed to obtain a total asteroid gravitational potential function.
It is understood that the details of each step in the method embodiments have already been described in the above system embodiments, and therefore will not be described herein.
The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention, and various modifications and changes may be made by those skilled in the art. Any modification, equivalent replacement, or improvement made within the spirit and principle of the present invention should be included in the protection scope of the present invention.
Claims (7)
1. A asteroid gravitational field full-autonomous measuring system based on ball satellite formation is characterized by comprising a ball satellite formation and a ground station, wherein the ball satellite formation moves under the action of the asteroid gravitational field, the ball satellite formation comprises a main satellite and a plurality of auxiliary satellites, the auxiliary satellites are respectively communicated with the main satellite, the main satellite is communicated with the ground station, and the main satellite is provided with a deep space autonomous navigation positioning system;
each slave satellite is used for measuring an inter-satellite vector between the slave satellite and the master satellite and an inter-satellite distance change rate between the slave satellite and other slave satellites, and transmitting the measurement result to the master satellite;
the main satellite is used for executing formation task autonomous operation based on self autonomous navigation position and speed and inter-satellite vector measurement results of a plurality of auxiliary satellites, and transmitting inter-satellite distance change rate measurement results of the plurality of auxiliary satellites to the ground station;
the ground station is used for inverting the asteroid gravitational field according to the received measurement results of the distance change rate between the satellites and establishing an expression of a gravitational field model;
the ground station establishes an expression of the asteroid gravitational field model in the following way:
firstly, a coordinate system is established by taking the mass center of the asteroid as an origin, a Brillouin ball which can contain all plastids of the asteroid is established by taking the origin as a sphere center, different gravitational potential expressions and potential coefficients are adopted for regions in the Brillouin ball and regions outside the Brillouin ball, wherein,
the minor planet gravitational potential outside the Brillouin sphere is as follows:
the asteroid gravitational potential in the Brillouin sphere is as follows:
wherein (r, theta, lambda) is the spherical coordinate of the particle on the asteroid in the body coordinate system, r is the distance between the particle and the origin of the coordinate system, theta is the included angle between the vector of the origin pointing to the particle and the positive direction of the z axis, lambda is the included angle between the projection vector of the origin pointing to the particle in the xy plane and the positive direction of the x axis, G is the universal gravitation constant, M is the mass of the asteroid, a is the radius of the Brillouin sphere,
is the minor planet gravitational potential coefficient outside the Brillouin sphere domain,
is the asteroid gravitational potential coefficient in the Brillouin sphere,
for fully normalized associated Legendre polynomials, K1、K2Is a coefficient, n is the order of the gravitational field model, and k is the number of times of the gravitational field model.
2. The asteroid gravitational field fully autonomous measurement system based on formation of spherical satellites of claim 1,
each slave satellite measures through an inter-satellite distance measuring instrument carried by the slave satellite to obtain an observed value of the inter-satellite distance change rate between the slave satellite and other slave satellites, measures through an accelerometer carried by the slave satellite to obtain the interference force received by the slave satellite or calculates through a high-precision model to obtain the interference force received by the slave satellite, and then eliminates the influence of the interference force from the observed value of the inter-satellite distance change rate to obtain a real value of the inter-satellite distance change rate under the action of a small planet gravitational field.
3. The asteroid gravitational field fully autonomous measurement system based on formation of spherical satellites of claim 2,
the ground station performs orbit integration by selecting a reference asteroid gravitational field model, a satellite perturbation force model and an initial state of a formation satellite, calculates the inter-satellite distance change rate of each satellite to be used as a reference value, and continuously adjusts the initial state parameters of the reference asteroid gravitational field model, the satellite perturbation force model and the formation satellite by iteration to enable the reference value of the inter-satellite distance change rate to continuously approach a true value, when the difference between the reference value and the true value of the inter-satellite distance change rate meets a task setting condition, the finally adjusted reference asteroid gravitational field model is the inversion gravitational field model.
4. The asteroid gravitational field fully autonomous measurement system based on formation of spherical satellites of claim 2,
the inter-satellite range finder comprises an inter-satellite laser range finder and/or an inter-satellite microwave range finder.
5. The asteroid gravitational field full-autonomous measurement method based on the formation of the ball satellites adopts the asteroid gravitational field full-autonomous measurement system based on the formation of the ball satellites as claimed in any one of claims 1-4, and is characterized by comprising the following steps:
measuring an inter-satellite vector between each slave satellite and the master satellite and an inter-satellite distance change rate between the slave satellites;
executing formation task autonomous operation based on autonomous navigation position and speed of the main satellite and inter-satellite vector measurement results of the main satellite and the auxiliary satellites;
inverting the asteroid gravitational field based on the measurement results of the distance change rate between a plurality of slave stars and the slave stars, and establishing an expression of a gravitational field model;
the step of establishing the expression of the gravitational field model specifically includes the following steps:
firstly, a coordinate system is established by taking the mass center of the asteroid as an origin, a Brillouin ball which can contain all plastids of the asteroid is established by taking the origin as a sphere center, different gravitational potential expressions and potential coefficients are adopted for regions in the Brillouin ball and regions outside the Brillouin ball, wherein,
the minor planet gravitational potential outside the Brillouin sphere is as follows:
the asteroid gravitational potential in the Brillouin sphere is as follows:
wherein (r, theta, lambda) is the spherical coordinate of the particle on the asteroid in the body coordinate system, r is the distance between the particle and the origin of the coordinate system, theta is the included angle between the vector of the origin pointing to the particle and the positive direction of the z axis, lambda is the included angle between the projection vector of the origin pointing to the particle in the xy plane and the positive direction of the x axis, G is the universal gravitation constant, M is the mass of the asteroid, a is the radius of the Brillouin sphere,
is the minor planet gravitational potential coefficient outside the Brillouin sphere domain,
is the asteroid gravitational potential coefficient in the Brillouin sphere,
for fully normalized associated Legendre polynomials, K1、K2Is a coefficient, n is the order of the gravitational field model, and k is the number of times of the gravitational field model.
6. The asteroid gravitational field full autonomous measurement method based on formation of spherical satellites of claim 5,
the step of measuring the inter-satellite distance change rate between the slave satellites specifically comprises the following steps:
measuring an observed value of an inter-satellite distance change rate between the slave satellites by using an inter-satellite distance measuring instrument;
measuring interference force received by the slave star by using an accelerometer or calculating the interference force received by the slave star through a high-precision model;
and eliminating the influence of interference force from the observed value of the change rate of the inter-satellite distance to obtain the true value of the change rate of the inter-satellite distance under the action of the asteroid gravitational field.
7. The asteroid gravitational field full autonomous measurement method based on formation of spherical satellites of claim 6,
the step of inverting the asteroid gravitational field based on the measurement results of the distance change rates among the plurality of satellites specifically comprises the following steps:
selecting a reference asteroid gravitational field model, a satellite perturbation force model and an initial state of a formation satellite for orbital integration, calculating to obtain the inter-satellite distance change rate of each satellite, and taking the inter-satellite distance change rate as a reference value;
and continuously adjusting the initial state parameters of the reference asteroid gravitational field model, the satellite perturbation force model and the formation satellites in an iterative manner to enable the reference value of the inter-satellite distance change rate to continuously approach the true value, and when the difference between the reference value and the true value of the inter-satellite distance change rate meets the task setting condition, finally adjusting the obtained reference asteroid gravitational field model to be the inversion gravitational field model.
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